Question

if b+c=2a then prove that cos(B-C/2)=sinA/2
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Answer 1

$b+c=2a </p><p></p><p>→ 2R \: sinB+2R \: sinC=4R \: sinA \\\\</p><p></p><p>→ sinB+sinC=2sinA \\\\</p><p></p><p>→ 2sin( \frac{b + c}{2} )cos( \frac{b - c}{2} )=4sin \frac{a}{2} \: cos \frac{a}{2} \\\\</p><p></p><p>→ sin( \frac{\pi - a}{2} )cos( \frac{b - c}{2} )=2sin \frac{a}{2} cos \frac{a}{2} \\\\</p><p></p><p>→ cos \frac{a}{2} cos( \frac{b - c}{2} )=2sin \frac{a}{2} cos \frac{a}{2} \\\\</p><p></p><p>→ cos( \frac{b - c}{2} )=2sin \frac{a}{2} \\\\</p><p></p><p>$

Answer 2

Answer:

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